We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an $n$-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].

Keywords: linear programming, duality, weak KAM theory

@article{COCV_2002__8__693_0, author = {Evans, L. C. and Gomes, D.}, title = {Linear programming interpretations of {Mather's} variational principle}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {693--702}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, doi = {10.1051/cocv:2002030}, zbl = {1090.90143}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2002030/} }

TY - JOUR AU - Evans, L. C. AU - Gomes, D. TI - Linear programming interpretations of Mather's variational principle JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 693 EP - 702 VL - 8 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2002030/ DO - 10.1051/cocv:2002030 LA - en ID - COCV_2002__8__693_0 ER -

%0 Journal Article %A Evans, L. C. %A Gomes, D. %T Linear programming interpretations of Mather's variational principle %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 693-702 %V 8 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2002030/ %R 10.1051/cocv:2002030 %G en %F COCV_2002__8__693_0

Evans, L. C.; Gomes, D. Linear programming interpretations of Mather's variational principle. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 693-702. doi : 10.1051/cocv:2002030. http://archive.numdam.org/articles/10.1051/cocv:2002030/

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